Determination of the lattice susceptibility within the dual fermion method

In this paper, we present the details of the dual fermion (DF) method to study the nonlocal corrections to the single-site dynamical mean-field theory (DMFT). The DMFT two-particle Green's function is calculated using continuous-time quantum Monte Carlo method. The momentum dependence of the vertex function is analyzed and its renormalization based on the Bethe-Salpeter equation is performed in the particle-hole channel. We found magnetic instability for both the dual and the lattice fermions. Furthermore, the lattice fermion susceptibility is calculated in this method and also in another recently proposed method, namely, dynamical vertex approximation (D Gamma A). The comparisons between these two methods are presented in both weak- and strong-coupling regions. Compared to the results from the quantum Monte Carlo calculation, the susceptibility obtained from the DF and D Gamma A methods are satisfactory.